What is expand (1/((s+1)^2)+2)*(-(s+1)) ?

The solution to expand (1/((s+1)^2)+2)*(-(s+1)) is -1/(s+1)-2s-2

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expand (1/((s+1)^2)+2)*(-(s+1))

expand

(\frac{1}{( s + 1 ) ^{2}} + 2) \cdot (- (s + 1))

- \frac{1}{s + 1} - 2 s - 2

Solution steps

(\frac{1}{( s + 1 ) ^{2}} + 2) (- (s + 1))

Apply rule:

a (- b) = - ab

(\frac{1}{( s + 1 ) ^{2}} + 2) (- (s + 1)) = - (\frac{1}{( s + 1 ) ^{2}} + 2) (s + 1)

= - (\frac{1}{( s + 1 ) ^{2}} + 2) (s + 1)

Apply FOIL method

(\frac{1}{( s + 1 ) ^{2}} + 2) (s + 1) : \frac{1}{s + 1} + 2 s + 2

= - (\frac{1}{s + 1} + 2 s + 2)

Apply the distributive law:

- (a + b) = - a - b

- (\frac{1}{s + 1} + 2 s + 2) = - \frac{1}{s + 1} - 2 s - 2

= - \frac{1}{s + 1} - 2 s - 2

\frac{x + 4}{( 3 x + 2 ) ( x - 8 )}

\frac{( 3 x + 4 ) ( x - 9 )}{( x - 2 ) ( x + 2 )}

\frac{1}{2} (x - 3)^{2} (x + 1)^{3}

\frac{4}{( s + 2 ) ^{2}}

\frac{( e ^{- s} + s ^{2} + s + 10 )}{( s + 4 ) ( s - 2 ) ( s - 1 )}

What is expand (1/((s+1)^2)+2)*(-(s+1)) ?
The solution to expand (1/((s+1)^2)+2)*(-(s+1)) is -1/(s+1)-2s-2